An Introduction to Graph Theory for Security People Who Can’t 'Math Good'

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An Introduction to Graph Theory for Security People Who Can’t Math Good Andrew Hay, CISSP

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Session Overview » A gentle introduction to graph theory » Graphs in every day life » Freely available tools » The application of graphs in a security context » Summary & Application

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A Gentle Introduction to Graph Theory

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If You’re Anything Like Me… » You completely zone out when you see something like this source: http://article.sapub.org/10.5923.j.am.20150505.01.html

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What Is A Graph? 0 1 2 3 4 5 A B C

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A Graph Is… » A graph is a collection of • vertices (i.e. nodes, dots) - where a vertex is an entity which represents some object (e.g. a person, a place, etc.) • edges (i.e. relationships, lines) - where an edge represents the relationship between two vertices source: http://tinkerpop.apache.org/

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A Graph Is (continued)… » Diagram above shows a graph with two vertices • One with a unique identifier of 1 • Another with a unique identifier of 3 » There is an edge connecting the two with a unique identifier of 9 » It is important to consider that the edge has a direction which goes out from vertex 1 and in to vertex 3 source: http://tinkerpop.apache.org/

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A Graph Is (continued)… » To give some meaning to this basic structure, vertices and edges can each be given labels to categorize them » You can now see that a vertex 1 is a person and vertex 3 is a software vertex source: http://tinkerpop.apache.org/

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A Graph Is (continued)… » They are joined by a created edge which allows you to see that a person created software » The label and the id are reserved attributes of vertices and edges, but you can add your own arbitrary properties as well source: http://tinkerpop.apache.org/

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What Is A Graph? 0 1 2 3 4 5 A B C

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So…What Is A Graph? Chart Graph Plot 0 1 2 3 4 5

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A Little More Advanced Graph Theory » You’ll often hear the words network and graph used interchangeably…and there is nothing wrong with that » If the edges in a network are directed (i.e. pointing in only one direction) the network is called a directed network or a directed graph, sometimes digraph for short » When drawing a directed network, the edges are typically drawn as arrows indicating the direction source: http://mathinsight.org/definition/network

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A Little More Advanced Graph Theory » If all edges are bidirectional, or undirected, the network is an undirected network (or undirected graph) source: http://mathinsight.org/definition/network

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A Little More Advanced Graph Theory » Variations • A small undirected network where the nodes and edges have different types, as indicated by their colors and line styles • A small directed network where the edges and nodes have different weights, as indicated by their sizes source: http://mathinsight.org/image/small_undirected_node_edge_types_network source: http://mathinsight.org/image/small_directed_weighted_nodes_edges_network

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Graphs In Every Day Life

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Graphs in Every Day Life: Internet » Everyone has seen a visual representation of the Internet » Often, colors indicate operator of network, country, etc. » Structure determined by sending a storm of IP packets out randomly across the network » Each packet is programmed to self-destruct after a delay, and when this happens, the packet failure notice reports back the path the packet took before it died source: http://mathinsight.org/image/internet_map_jurvetson_2004

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Graphs in Every Day Life: TSP » Travelling salesman problem (TSP) • "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?” source: https://www.mathworks.com/help/optim/examples/travelling-salesman-problem.html

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Graphs in Every Day Life: More Examples… » Mapping • Google maps, self-driving cars, etc. • “Hey, Siri, how do I get to 1 Main Street?” » Perception/Attitude Analysis • What hashtags are trending right now? • Which Presidential candidate is being talked about most on which social media platform? » And, of course, security! source: https://datasemantics.files.wordpress.com/2013/12/graph3.png

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Freely Available Tools Including clients, databases, and programming modules

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Tools: Google Fusion Tables » support.google.com/fusiontables/answer/2566732 ?hl=en – Network Graph • Basic network mapping tool • Some useful filter functionality • Lacks the deep customization options and analysis functionality • Can produce insightful visualizations » developers.google.com/fusiontables • Create, update, and delete tables and table data • Issue SQL-like queries

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Tools: Graphviz » www.graphviz.org • Open source graph visualization software • The Graphviz layout programs take descriptions of graphs in a simple text language, and make diagrams in useful formats - Images, SVG, PDF, Postscript , interactive graph browser • Many useful features for diagrams - options for colors, fonts, tabular node layouts, line styles, hyperlinks, and custom shapes source: http://www.graphviz.org/content/profile

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Tools: Visual Investigate Scenarios (VIS) » vis.occrp.org • Designed to assist investigative journalists, activists and others in mapping complex business or crime networks • Help investigators understand and explain corruption, organized crime and other wrongdoings and to translate complex narratives into simple, universal visual language • Customizable, dynamic html5 visualization templates • Illustrate entities, networks and complex configurations of data

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Tools: Gephi » gephi.org • Desktop tool for performing powerful network analysis and creating network visualizations • Described as being like Photoshop™ but for graph data • The user interacts with the representation, manipulate the structures, shapes and colors to reveal hidden patterns • Designed to help data analysts to make hypothesis, intuitively discover patterns, isolate structure singularities or faults during data sourcing source: https://gephi.org/screenshots/

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Tools: OpenGraphiti » www.opengraphiti.com • OpenGraphiti is a free and open source 3D data visualization engine created by Thibault Reuille of OpenDNS • Designed for data scientists to visualize semantic networks and to work with them • It offers an easy-to-use API with several associated libraries to create custom-made datasets

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Tools: Maltego » www.paterva.com/web7/buy/malte go-clients/maltego-ce.php • Maltego CE is the community editio • Available for free for everyone after a quick registration • Interactive data mining tool • Renders directed graphs for link analysis • Used in online investigations for finding relationships between pieces of information from various sources located on the Internet source: www.paterva.com

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Tools: Maltego (continued…) » www.paterva.com/web7/buy/malte go-clients/casefile.php • CaseFile is Paterva's answer to the offline intelligence problem • Allows for analysts to examine links between offline data • Same graphing application as Maltego without the ability to run transforms • CaseFile gives you the ability to quickly add, link and analyze data source: www.paterva.com

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Graph Databases: neo4j » neo4j.com • Graph database management system developed by Neo Technology, Inc • ACID-compliant transactional database with native graph storage and processing • Implemented in Java • Accessible from software written in other languages using the Cypher Query Language • Exposes a transactional HTTP endpoint source: https://neo4j.com/

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Graph Databases: OrientDB » orientdb.com • Open source NoSQL database management system • Written in Java • Multi-model database, supporting graph, document, key/value, and object models • Relationships are managed as in graph databases with direct connections between records • Supports schema-less, schema-full, and schema-mixed modes source: http://orientdb.com/orientdb/

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Graph Databases: Titan » titan.thinkaurelius.com • Scalable graph database optimized for - Storing and querying graphs - Containing hundreds of billions of vertices and edges - Distributed across a multi-machine cluster • Support for various storage backends • Support for global graph data analytics, reporting, and ETL through integration with big data platforms • Native integration with the TinkerPop graph stack source: http://titan.thinkaurelius.com/

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Graph Stack: Apache TinkerPop » tinkerpop.apache.org • Open source Graph Computing Framework • Goal is to make it easy for developers to create graph applications by providing APIs and tools that simplify their endeavors • Abstraction layer over different graph databases and different graph processors • As an abstraction layer, TinkerPop provides a way to avoid vendor lock-in to a specific database or processor source: https://tinkerpop.apache.org/

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Development Modules » NetworkX • networkx.github.io • Package for the creation, manipulation, and study of the structure, dynamics, and functions of complex networks » Graph-tool • graph-tool.skewed.de • Manipulation and statistical analysis of graphs » SNAP for Python • snap.stanford.edu/snappy/ • General purpose, high performance system for analysis and manipulation of large networks • Written in C++ and optimized for maximum performance and compact graph representation • Scales to massive networks with hundreds of millions of nodes, and billions of edges

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Development Modules » semanticnet • github.com/ThibaultReuille/semanticnet • Small python library to create semantic graphs in JSON • Datasets can then be visualized with OpenGraphiti » Plotly for Python • plot.ly/ipython- notebooks/network-graphs • Store position as node attribute data • Add, change, delete nodes, node color, connections, etc.

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Development Modules » vis.js • visjs.org • Designed to be easy to use, to handle large amounts of dynamic data, and to enable manipulation of and interaction with the data » sigmajs • sigmajs.org • Allows developers to integrate network exploration in rich Web applications » JSNetworkX • jsnetworkx.org • JavaScript port of the NetworkX graph library » Cytoscape.js • js.cytoscape.org • Fully featured graph library written in pure JS • Designed for users first, for both front facing app and developer use cases

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The Application Of Graphs In A Security Context

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Scenario: Incident Response The Application Of Graphs In A Security Context

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Scenario: Incident Response » “We had a data breach, what was taken, and who was involved?” Mary Rahim Stu SSN CC

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Scenario: Incident Response Mary Rahim Stu SSN CC » “We had a data breach, what was taken, and who was involved?”

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Scenario: Incident Response Stu SSN CC HTTP Proxy upload download » “We had a data breach, what was taken, and who was involved?”

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Scenario: Incident Response Stu SSN CC HTTP Proxy upload download » “We had a data breach, what was taken, and who was involved?”

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Scenario: Incident Response » What would this look like in a tool? » Using Google’s experimental Fusion Tables we can easily graph this » Easy to show links, directionality, and node colors

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Scenario: Incident Response » Type by Name shows who has interacted with what data

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Scenario: Incident Response » Action by Name shows who has performed what actions

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Scenario: Actor Tracking The Application Of Graphs In A Security Context

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Scenario: Actor Tracking » “New Phishing Campaign Targets South-East Asia”* • http://www.minerva-labs.com/post/new-phishing- campaign-targets-south-east-asia » Malware variant that was distributed via phishing emails in south-east Asia. » The binary mimicked Navicat and had multiple info- stealing capabilities - and possibly a later stage POS oriented module. * source: https://app.threatconnect.com/auth/incident/incident.xhtml?incident=3440670

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Scenario: Actor Tracking » Let’s load the indicators of compromise (IOC) from the blog post into a tool » This time, we’ll use Maltego Community Edition (CE) source: www.paterva.com

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Scenario: Actor Tracking » Add the various elements that you want to track • Hashes • Domains • IP addresses • Email addresses • etc.

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Scenario: Actor Tracking » Use the transforms to enrich the data • VirusTotal Public • ThreatCrowd • PassiveTotal - Get Passive DNS with Time - Get Whois Details - Whois Search by Email Address » Avoid running “All Transforms”

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Scenario: Actor Tracking » asdf

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Scenario: Actor Tracking » Zooming in we can see interesting associations…like how the malware hashes are being recognized

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Scenario: Actor Tracking » Zooming in we can see interesting associations…like how the domains are associated with the same registrant email address

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Scenario: Actor Tracking » Zooming in we can see interesting associations…like how the domains are associated with the same and IP address

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Scenario: Actor Tracking » We can also enrich the data with…all of the other domains registered using that email address

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Scenario: Actor Tracking » As you can imagine, this can quickly get out of hand…

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General Suggestions » Just because you CAN graph or run a transform on something… » Consider using only the data you need for a particular task or project » If you want to experiment with different transforms, data points, nodes, edges, etc…

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Summary & Application

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Summary » The general application of graph theory doesn’t require an advanced degree in mathematics • Especially once you know the basics » The connection of related information (read: nodes & edges) helps represent the data • Both visually and programmatically » There are a growing number of tools to help create graph associations, store graph data, and programmatically traverse and modify said data • Pick what works best for you and your environment source: https://en.wikipedia.org/wiki/Travelling_salesman_problem

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Apply What You Have Learned Today » Next week you should: • Take a look at the various free tools and see which one(s) resonate » In the first three months following this presentation you should: • Begin graphing connections for a simple project (e.g. threat actor tracking) • Use your graph project to teach your team or peers the value » Within six months you should: • Have a firm grasp of your own graph project • Look to introduce graph relationships, where applicable, to current security projects

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Thank You, Questions? » Andrew Hay, CISSP » Co-Founder & CTO, LEO Cyber Security • email: andrew.hay@leocybersecurity.com • mobile: +1.415.940.9660 • twitter: @andrewsmhay • linkedin: http://www.linkedin.com/in/andrewhay • schedule a meeting: https://ahay.acuityscheduling.com

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